What does ‘sweep’ mean in the context “The Taliban swept to power”

Although the phrase can mean that, and often does, it's also sometimes applied in a more broad context. To be "swept off your feet" is to be surprised, enthralled, exhilarated. Critics can be swept off their feet by an epic film; operagoers can be swept off their feet by a beautiful aria, etc.

As for how sweeping became associated with love, that's referring to the aspect of sweeping that means a smooth movement, not the act of using a broom. Ballroom dancers can sweep across the dance floor, a powdery snow can sweep across the barren fields. It's that smooth, fluid motion – and the idea of your emotions being carried in that fashion – that brought about the idiom. A strong ocean or river current can literally sweep you off your feet, and young lovers can do the same thing to each other, figuratively and emotionally.

As mentioned in the previous answer, Y/Y is likely to be an abbreviation of the phrase year-over-year. (Or sometimes year-on-year.) Typically, a number before the phrase states a difference or ratio of one year's value of some statistic to the previous year's value.

For example, in wikipedia's “Plug in electric vehicle” article, we find

During the first seven months of 2014 the plug-in hybrid segment in the German market experienced a growth of 454% year-over-year.

This indicates that the 2014 value for plug-in hybrids registered during January through July is 1 + 4.54 or 5.54 times as much as the same statistic for 2013. (The added 1 is due to 454% being the amount of growth, ie a difference rather than a ratio.)

In the examples given in the question, “+14x” stands for “up by 14 times” and “+15x” stands for “up by 15 times”. (It isn't clear to me whether they mean incremented by 14 times the previous value, or equal to 14 times the previous value.)

Edit: As an abbreviation of year-over-year, YOY may be more common than Y/Y. See investopedia.com and lexicon.ft.com for examples of use.